Question

HELP PLEASE!!!

1. Answer the questions by drawing on the coordinate plane below. (2 Points possible)

(a) Draw the image of ∆JKL after a rotation of 90°counterclockwise about the origin. Label the image
∆J′K′ L′.

(b) Draw the image of ∆JKL after a reflection across the y-axis. Label the image ∆J′′K′′L′′..

Answer 1

90 degrees counterclockwise

Invert the x and y points and the y becomes negative (x, y) --------> (-y, x).

J( -4, 1) becomes (-1,-4)

K( -4,-2) becomes (2,-4)

L (-3,-1) becomes (1,-3)

reflection across the y axis

the x becomes negative (x, y) --------> (-x, y).

J( -4, 1) becomes (4,-1)

K( -4,-2) becomes (4,-2)

L (-3,-1) becomes (3,1)

Answer 2

(a) The vertices of image are J'(-1,-4), K'(2,-4) and L'(1,-3).

(b) The vertices of image are J''(4,1), K''(4,-2) and L''(3,-1).

Explanation:

From the given figure it is clear that J(-4,1), K(-4,-2) and L(-3,-1).

(a)

If a figure rotated 90°counterclockwise about the origin, then

`(x,y)\rightarrow (-y,x)`

The vertices of image of ∆JKL after a rotation of 90°counterclockwise about the origin are

`J(-4,1)\rightarrow J'(-1,-4)`

`K(-4,-2)\rightarrow K'(2,-4)`

`L(-3,-1)\rightarrow L'(1,-3)`

Therefore the vertices of image are J'(-1,-4), K'(2,-4) and L'(1,-3).

(b)

If a figure reflected across the y-axis, then

`(x,y)\rightarrow (-x,y)`

The vertices of image of ∆JKL after a reflection across the y-axis are

`J(-4,1)\rightarrow J''(4,1)`

`K(-4,-2)\rightarrow K''(4,-2)`

`L(-3,-1)\rightarrow L''(3,-1)`

Therefore the vertices of image are J''(4,1), K''(4,-2) and L''(3,-1).